Lower bound for the Complexity of the Boolean Satisfiability Problem

TL;DR

This paper establishes that the Boolean Satisfiability Problem inherently requires exponential time to solve, indicating no efficient algorithms exist for this NP-complete problem.

Contribution

It introduces a novel reformulation as a lottery for an extreme case, providing a new approach to analyze the problem's complexity.

Findings

Boolean Satisfiability Problem requires exponential time

Reformulation as a lottery reveals stable complexity around 2^n

No efficient algorithm exists for NP class problems

Abstract

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery for an extreme case is presented to determine a stable complexity around $2^n$. The reformulation point out that the decision Boolean Satisfiability Problem can only be solved in exponential time. This implies there is not an efficient algorithm for the NP Class.